Does that mean that between those 7,000 light-years, there's absolute nothing in the way that obscures the pillars? Given it's arcseconds, I'd expect that any kind of disturbance would make it simply impossible to visualize it.
Almost, with a few details.
It means there's nothing opaque in the way. At risk of being trite, the telescope lens and the atmosphere (well, not for Hubble) is often "in the way", but they're transparent. Many substances are opaque only in some wavelengths and transparent in others. Astronomical photographs are sometimes not literally what you would see with your eye, they are false-color.
While it may seem amazing that no object happens to be in a 7k lyr cone, keep in mind that's not the "experiment". It is actually an infinitely long cone and we see only the first object. For example, there could be an object directly behind Proxima Centauri, and we wouldn't see it. So the true "property" is the distribution of distances to the foremost object in each cone coming out of the telescope. This distribution is generally as you would expect given the number, size and type of objects you find in the universe.
Of course if there was actually an object behind Proxima Centauri, we could still detect it as it moves around (and we do) - it would eventually "peek out". Incidentally, other planets, the Moon, the Earth, the Sun often obscure celestial bodies - but not all the time. But if by unlikely coincidence the obstacle's orbit was in perfect sync with the telescope and the obstacle, we might still be able to detect it due to gravity bending light around the obstacle.
So in sum:
- Not every obstacle blocks every wavelength
- Most objects (including us) are moving so they are not always permanently obscured
- Even objects that are truly obscured can still be observed indirectly
- Objects that are truly obscured are unknown to us, therefore you can't rightly marvel at how few of them there are, since you don't rightly know if there's few or many